Question

given the following information, determine which lines, if any, are parallel. state the converse that justifies your answer.

Answer 1

From the information in the diagram found in a similar question online (please see attached drawing), the parallel lines are;

1. w||z
2. x||y
3. x||y
4. w||z
5. w||z
6. x||y
7. x||y
8. w||z
9. x||y
10. w||z

What are the relationships between angles formed by parallel lines?

Parallel lines are lines that do not meet, when extended indefinitely.

The possible information given as obtained from a similar question posted online are;

1. ‹1 is congruent to ‹5

2. ‹7 is congruent to ‹9

3. m‹8 + m‹9 = 180°

4. ‹16 is congruent to ‹14

5. m‹1 + m‹4 = 180°

6. ‹3 is congruent to ‹13

7. ‹2 is congruent to ‹10

8. ‹11 is congruent to ‹15

9. m‹4 + m‹13 = 180°

10. ‹8 is congruent to ‹6

1. Given that ‹1 is congruent to ‹5 where ‹1 and ‹5 are alternate exterior angles, we have that line w is parallel to line z

• w||z

Theorem (converse); Alternate exterior angles formed by two parallel lines having a common transversal are congruent.

2. ‹7 and ‹9 are alternate interior angles.

Given that ‹7 is congruent to ‹9, therefore;

Line x is parallel to line y

• x||y

Theorem (converse); Alternate interior angles formed by two parallel lines having a common transversal are congruent.

3. Given that m‹8 + m‹9 = 180°, therefore;

‹8 and ‹9 are supplementary angles, formed between lines x and y.

‹8 and ‹9 are also consecutive interior angles.

Theorem (converse); Consecutive interior angles formed between parallel lines are supplementary.

Therefore;

• x||y

4. ‹16 and ‹14 are corresponding angles formed by lines w and z.

Theorem (converse); Corresponding angles formed by parallel lines are congruent.

Given ‹16 congruent to ‹14, we have;

• w||z

5. m‹1 and m‹4 are consecutive exterior angles formed by lines w and z.

Theorem (converse); Consecutive exterior angles formed by two parallel lines are supplementary.

Given that m‹1 + m‹4 = 180°, we have;

• w||z

6. ‹3 and ‹13 are alternate exterior angles formed by lines x and y.

Theorem (converse); Alternate exterior angles formed by parallel lines are congruent.

Given that ‹3 congruent to ‹13, we have;

• x||y

7. ‹2 and ‹10 are corresponding angles formed by lines x and y

Given that ‹2 congruent to ‹10, therefore;

• x||y

8. ‹11 and ‹15 are alternate interior angles formed by lines w and z.

‹11 is congruent to ‹15, therefore;

• w||z

9. ‹4 and ‹13 are consecutive exterior angles formed by lines x and y

m‹4 + m‹13 = 180°, therefore;

• x||y

10. ‹8 and ‹6 are corresponding angles formed by lines w and z.

‹8 is congruent to ‹6, therefore;

• w||z

Learn more about angles formed by parallel lines that have a common transversal here:

brainly.com/question/24607467

#SPJ1